The long division method in finding the square root of a polynomial is useful when the degree of the polynomial is higher.

**Finding the Square Root of a Polynomial by Division Method**

The long division method
in finding the square root of a polynomial is useful when the degree of the
polynomial is higher.

Find the square root of** **64*x*^{4}** **−** **16*x*^{3} +
17*x* ^{2} − 2*x* + 1

**Note**

Before proceeding to
find the square root of a polynomial, one has to ensure that the degrees of the
variables are in descending or ascending order.

**Example 3.22 **Find the square root of
the expression

If** **9*x*^{4}** **+** **12*x*^{3}** **+** **28*x*^{2}** **+** ***ax*** **+*b*** **is a perfect square,
find the values of** ***a*** **and** ***b*.

Because the given
polynomial is a perfect square *a* − 16 = 0 , *b* − 16 = 0 Therefore *a*
= 16 , *b* = 16 .

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